Calculating matters less than setting up math problems

carpenters have to know how to set up math problemsAsk an elementary school child “What is math?” and you’re likely to get an answer something like: “it’s problems….addition, subtraction, multiplication, division.” 

That’s what math feels like in school: rules and procedures that you follow to solve problems. It’s too bad, because that’s not what math means to adults in the real world.

Math problems start with questions

When carpenters, engineers, lawyers, architects, and accountants use math, they start with a question. For example: 

  • The carpenter might ask: how far from the left wall is the left edge of the new window?
  • The engineer might ask: should I make a particular bike part out of steel or aluminum?
  • The accountant might ask: what kind of crisis could cause this organization to go bankrupt?

Next, they turn their real-world problem into a math problem. For example the carpenter knows that the centerline of the window should be placed ⅔ of the way from the left wall toward the right wall. The wall is nine feet wide. The new window is two feet wide. 

Now he turns his real-world question into a math problem: 

Distance from left wall = (⅔ X 9) – (2-1)

The answer is 5 feet. 

The engineer thinks about her problem some more. Steel is stronger. Aluminum is lighter, but also more expensive. Her math equations are more complicated than the carpenter’s. 

The accountant knows that the company has $1 million of cash on hand and is spending $500,000 per month. What kind of crisis could cause what kind of decrease in revenue? If revenue decreased by a particular amount, how much would expenses decrease? To answer his question, he’ll develop some equations that are more complex than the carpenter’s, but simpler than the engineer’s.

With the problem set up, each of them does some calculations to get an answer.

Does the answer we calculated really answer our question?

Then, after they get their answer, they’ll think about it for a little while. Did the answer they calculated really answer their question? For the carpenter, it’s a quick check. The engineer and accountant have to work a little harder. Does their equation capture what’s important? Is there a different and better way to think about the question, which would lead to a different calculation and answer?

In all three cases, we can summarize the process in four steps:

  1. Pose a real-world question
  2. Translate the real-world question into a math problem
  3. Calculate the answer
  4. Consider: did we answer the question? Is there a better way to answer it?

In all cases, step three, calculating, is the easiest part. The carpenter can do the problem in his head. The engineer will probably use a computer. The accountant might use a spreadsheet.

Setting up math problems is the most interesting and challenging part

Steps two and four are the more challenging and interesting parts of the process for everyone. The second step involved translating a real-world question into a math problem. The fourth step involved thinking about whether the answer we got is a good answer to our original question. If not, we try again.

If you want your child to grow up engaged with mathematics — and you do! — introduce them to parts one, two of this four-part process at an early age. Instead of giving them worksheets, draw them into real-world questions and talk about them.

Ask your first grader questions like: “We need to bring enough dog food for our weekend away. Could you do that?” Ask your third grader question like: “Do you think we have enough eggs to last until the weekend? “

Inspire your child to ask their own math-related questions

As your child gets older, look for ways to engage them with mathematical thinking on topics that interest them. Let’s say you have a soccer player. You could ask them: how far ahead of a teammate do you kick the ball? How do they know where to aim? 

Through conversation, see if you can inspire them to translate these kinds of real-world questions into simple math problems. Then, when they get an answer, you can ask: is this a good answer? Is there a way to make the answer better? They may struggle a bit at first, and you may need to give them some help along the way.

With this kind of conversation, you’re laying the groundwork for your child to understand and engage with math like adults do in the real world.

Calculating matters less than setting up math problems